Line data Source code
1 0 : // Distributed under the MIT License.
2 : // See LICENSE.txt for details.
3 :
4 : #pragma once
5 :
6 : #include <cstddef>
7 :
8 : #include "DataStructures/Tensor/Tensor.hpp"
9 : #include "Utilities/Gsl.hpp"
10 :
11 : namespace CurvedScalarWave::Worldtube {
12 :
13 : namespace detail {
14 : void check_positive_time_and_timescale(double t_minus_turn_on,
15 : double turn_on_timescale);
16 :
17 : } // namespace detail
18 :
19 : /// @{
20 : /*!
21 : * \brief Computes the coordinate acceleration due to the scalar self-force onto
22 : * the charge.
23 : *
24 : * \details It is given by
25 : *
26 : * \begin{equation}
27 : * (u^0)^2 \ddot{x}^i_p = \frac{q}{\mu}(g^{i
28 : * \alpha} - \dot{x}^i_p g^{0 \alpha} ) \partial_\alpha \Psi^R
29 : * \end{equation}
30 : *
31 : * where $\dot{x}^i_p$ is the position of the scalar charge, $\Psi^R$ is the
32 : * regular field, $q$ is the particle's charge, $\mu$ is the particle's mass,
33 : * $u^\alpha$ is the four-velocity and $g^{\alpha \beta}$ is the inverse
34 : * spacetime metric in the inertial frame, evaluated at the position of the
35 : * particle. An overdot denotes a derivative with respect to coordinate time.
36 : * Greek indices are spacetime indices and Latin indices are purely spatial.
37 : * Note that the coordinate geodesic acceleration is NOT included.
38 : */
39 : template <size_t Dim>
40 1 : void self_force_acceleration(
41 : gsl::not_null<tnsr::I<double, Dim>*> self_force_acc,
42 : const Scalar<double>& dt_psi_monopole,
43 : const tnsr::i<double, Dim>& psi_dipole,
44 : const tnsr::I<double, Dim>& particle_velocity, double particle_charge,
45 : double particle_mass, const tnsr::AA<double, Dim>& inverse_metric,
46 : const Scalar<double>& dilation_factor);
47 :
48 : template <size_t Dim>
49 1 : tnsr::I<double, Dim> self_force_acceleration(
50 : const Scalar<double>& dt_psi_monopole,
51 : const tnsr::i<double, Dim>& psi_dipole,
52 : const tnsr::I<double, Dim>& particle_velocity, double particle_charge,
53 : double particle_mass, const tnsr::AA<double, Dim>& inverse_metric,
54 : const Scalar<double>& dilation_factor);
55 :
56 : /// @}
57 : /*!
58 : * \brief Computes the scalar self-force per unit mass
59 : *
60 : * \details It is given by
61 : * \begin{equation}
62 : * f^\alpha = \frac{q}{\mu} (g^{\alpha \beta} + u^\alpha u^\beta) \partial_\beta
63 : * \Psi^R
64 : * \end{equation}
65 : * where $\Psi^R$ is the regular field at the position of the particle, $q$ is
66 : * the particle's charge, $\mu$ is the particle's mass, $u^\alpha$ is the
67 : * four-velocity and $g^{\alpha \beta}$ is the inverse spacetime metric in the
68 : * inertial frame, evaluated at the position of the particle.
69 : */
70 : template <size_t Dim>
71 1 : tnsr::A<double, Dim> self_force_per_mass(
72 : const tnsr::a<double, Dim>& d_psi,
73 : const tnsr::A<double, Dim>& four_velocity, double particle_charge,
74 : double particle_mass, const tnsr::AA<double, Dim>& inverse_metric);
75 :
76 : /*!
77 : * \brief Computes the first time derivative of scalar self-force per unit mass,
78 : * see `self_force_per_mass`, by applying the chain rule.
79 : */
80 : template <size_t Dim>
81 1 : tnsr::A<double, Dim> dt_self_force_per_mass(
82 : const tnsr::a<double, Dim>& d_psi, const tnsr::a<double, Dim>& dt_d_psi,
83 : const tnsr::A<double, Dim>& four_velocity,
84 : const tnsr::A<double, Dim>& dt_four_velocity, double particle_charge,
85 : double particle_mass, const tnsr::AA<double, Dim>& inverse_metric,
86 : const tnsr::AA<double, Dim>& dt_inverse_metric);
87 :
88 : /*!
89 : * \brief Computes the second time derivative of scalar self-force per unit
90 : * mass, see `self_force_per_mass`, by applying the chain rule.
91 : */
92 : template <size_t Dim>
93 1 : tnsr::A<double, Dim> dt2_self_force_per_mass(
94 : const tnsr::a<double, Dim>& d_psi, const tnsr::a<double, Dim>& dt_d_psi,
95 : const tnsr::a<double, Dim>& dt2_d_psi,
96 : const tnsr::A<double, Dim>& four_velocity,
97 : const tnsr::A<double, Dim>& dt_four_velocity,
98 : const tnsr::A<double, Dim>& dt2_four_velocity, double particle_charge,
99 : double particle_mass, const tnsr::AA<double, Dim>& inverse_metric,
100 : const tnsr::AA<double, Dim>& dt_inverse_metric,
101 : const tnsr::AA<double, Dim>& dt2_inverse_metric);
102 :
103 : /*!
104 : * \brief Computes the covariant derivative of the scalar self-force per unit
105 : * mass $f^\alpha$, see `self_force_per_mass`, along the four velocity
106 : * $u^\beta$, i.e. $u^\beta \nabla_\beta f^\alpha$.
107 : */
108 : template <size_t Dim>
109 1 : tnsr::A<double, Dim> Du_self_force_per_mass(
110 : const tnsr::A<double, Dim>& self_force,
111 : const tnsr::A<double, Dim>& dt_self_force,
112 : const tnsr::A<double, Dim>& four_velocity,
113 : const tnsr::Abb<double, Dim>& christoffel);
114 : /*!
115 : * \brief Computes the time derivative of the covariant derivative of the scalar
116 : * self-force per unit mass $f^\alpha$, see `Du_self_force_per_mass`, along the
117 : * four velocity $u^\beta$, i.e.
118 : * $\frac{d}{dt}u^\beta \nabla_\beta f^\alpha$.
119 : */
120 : template <size_t Dim>
121 1 : tnsr::A<double, Dim> dt_Du_self_force_per_mass(
122 : const tnsr::A<double, Dim>& self_force,
123 : const tnsr::A<double, Dim>& dt_self_force,
124 : const tnsr::A<double, Dim>& dt2_self_force,
125 : const tnsr::A<double, Dim>& four_velocity,
126 : const tnsr::A<double, Dim>& dt_four_velocity,
127 : const tnsr::Abb<double, Dim>& christoffel,
128 : const tnsr::Abb<double, Dim>& dt_christoffel);
129 :
130 : /*!
131 : * \brief A function used to roll-on the self-force continuously from 0 to 1
132 : *
133 : * \details It is given by Eq.(60) of \cite Wittek:2024gxn
134 : * \begin{equation}
135 : * w(t) = 1 - \exp \left( - \left( (t - t_{\mathrm{turn_on}}) / \sigma \right)^4
136 : * \right), \end{equation} where $t$ is the current simulation time,
137 : * $t_{\mathrm{turn_on}}$ is the time where the self-force is turned on and
138 : * $\sigma$ dictates the timescale over which it is turned on. The function is
139 : * $\mathcal{C}^3$, i.e. three times continuously differentiable, assuming $w(t)
140 : * = 0$ for $t < t_{\mathrm{turn_on}}$.
141 : */
142 1 : double turn_on_function(double t_minus_turn_on, double turn_on_timescale);
143 :
144 : /*!
145 : * \brief The first derivative of `turn_on_function`
146 : */
147 1 : double dt_turn_on_function(double t_minus_turn_on, double turn_on_timescale);
148 :
149 : /*!
150 : * \brief The second derivative of `turn_on_function`
151 : */
152 1 : double dt2_turn_on_function(double t_minus_turn_on, double turn_on_timescale);
153 :
154 : } // namespace CurvedScalarWave::Worldtube
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